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We verify that the recently proven infinite families of holographic entropy
inequalities are maximally tight, i.e. they are facets of the holographic
entropy cone. The proof is technical but it offers some heuristic insight. On
star graphs, both families of inequalities quantify how concentrated / spread
information is with respect to a dihedral symmetry acting on subsystems. In
addition, toric inequalities viewed in the K-basis show an interesting
interplay between four-party and six-party perfect tensors.
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